Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks - INSPIRE

DataBETA

Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks

Mario Boneberg
(
- Tubingen U.
)
,
Federico Carollo
(
- Tubingen U.
)
,
Igor Lesanovsky
(
- Tubingen U. and
- Nottingham U.
)

Apr 21, 2023

17 pages

Published in:

New J.Phys. 25 (2023) 9, 093020

Published: Sep 8, 2023

e-Print:

2304.11209 [cond-mat.stat-mech]

DOI:

10.1088/1367-2630/aceff4

View in:

ADS Abstract Service

reference search2 citations

Citations per year

Abstract: (IOP)

Classical artificial neural networks, built from elementary units, possess enormous expressive power. Here we investigate a quantum neural network (QNN) architecture, which follows a similar paradigm. It is structurally equivalent to so-called (1+1)D quantum cellular automata, which are two-dimensional quantum lattice systems on which dynamics takes place in discrete time. Information transfer between consecutive time slices—or adjacent network layers—is governed by local quantum gates, which can be regarded as the quantum counterpart of the classical elementary units. Along the time-direction an effective dissipative evolution emerges on the level of the reduced state, and the nature of this dynamics is dictated by the structure of the elementary gates. We show how to construct the local unitary gates to yield a desired many-body dynamics, which in certain parameter regimes is governed by a Lindblad master equation. We study this for small system sizes through numerical simulations and demonstrate how collective effects within the quantum cellular automaton can be controlled parametrically. Our study constitutes a step towards the utilization of large-scale emergent phenomena in large QNNs for machine learning purposes.

Note:

17 pages, 3 figures

open quantum systems
quantum cellular automata
quantum neural networks
neural network: quantum
cellular automaton: quantum
time: discrete
gate: quantum
dimension: 2
many-body problem
network

References(93)

Figures(3)

[1]

Quantum Simulation

I.M. Georgescu
(
- Wako, RIKEN
)
,
S. Ashhab
(
- Wako, RIKEN
)
,
Franco Nori
(
- Wako, RIKEN and
- Michigan U. and
- Korea U.
)

- Rev.Mod.Phys. 86 (2014) 153
•
e-Print:
- 1308.6253
•
DOI:
- 10.1103/RevModPhys.86.153

[2]

Quantum Simulators: Architectures and Opportunities

Ehud Altman
(
- UC, Berkeley
)
,
Kenneth R. Brown
(
- Duke U.
)
,
Giuseppe Carleo
(
- New York U., CCPP
)
,
Lincoln D. Carr
(
- Colorado School of Mines
)
,
Eugene Demler
(
- Harvard U.
)

et al.

- PRX Quantum 2 (2021) 1, 017003,
- PRX Quantum 2 (2021) 017003
•
e-Print:
- 1912.06938
•
DOI:
- 10.1103/PRXQuantum.2.017003

[3]

Is Quantum Advantage the Right Goal for Quantum Machine Learning?

- PRX Quantum 3 (2022) 3, 030101
•
e-Print:
- 2203.01340
•
DOI:
- 10.1103/PRXQuantum.3.030101

[4]

The quest for a Quantum Neural Network

Maria Schuld
(
- KwaZulu Natal U.
)
,
Ilya Sinayskiy
(
- KwaZulu Natal U.
)
,
Francesco Petruccione
(
- KwaZulu Natal U.
)

- Quant.Inf.Proc. 13 (2014) 11, 2567-2586
•
DOI:
- 10.1007/s11128-014-0809-8

[5]

Machine Learning with Quantum Computers

M. Schuld
,
F. Petruccione

[6]

Quantum machine learning

Jacob Biamonte
(
- Skoltech and
- Waterloo U.
)
,
Peter Wittek
(
- ICFO, Barcelona
)
,
Nicola Pancotti
(
- Munich, Max Planck Inst. Quantenopt.
)
,
Patrick Rebentrost
(
- MIT
)
,
Nathan Wiebe
(
- Microsoft, Redmond
)

et al.

- Nature 549 (2017) 7671, 195-202
•
e-Print:
- 1611.09347
•
DOI:
- 10.1038/nature23474

Evaluating the performance of sigmoid quantum perceptrons in quantum neural networks

e-Print:
- 2208.06198

No Free Lunch for Quantum Machine Learning

Kyle Poland
(
- Leibniz U., Hannover
)
,
Kerstin Beer
(
- Leibniz U., Hannover
)
,
Tobias J. Osborne
(
- Leibniz U., Hannover
)

e-Print:
- 2003.14103

[9]

D. Wolpert
,
W. Macready

- IEEE Trans.Evol.Comput. 1 (1997) 67-82
•
DOI:
- 10.1109/4235.585893

[10]

An overview of quantum cellular automata

Pablo Arrighi
(
- LIS, Marseille and
- IXXI, Lyon
)

- Natural Comput. 18 (2019) 4, 885-899
•
e-Print:
- 1904.12956
•
DOI:
- 10.1007/s11047-019-09762-6

[11]

A review of Quantum Cellular Automata

Terry Farrelly
(
- Hannover U. and
- Queensland U.
)

- Quantum 4 (2020) 368
•
e-Print:
- 1904.13318
•
DOI:
- 10.22331/q-2020-11-30-368

[12]

Theory of Self-Reproducing Automata

J. von Neumann

[13]

Statistical Mechanics of Cellular Automata

Stephen Wolfram
(
- Caltech
)

- Rev.Mod.Phys. 55 (1983) 601
•
DOI:
- 10.1103/RevModPhys.55.601

[14]

Quantum Cellular Automata, Tensor Networks, and Area Laws

- Phys.Rev.Lett. 125 (2020) 19, 190402
•
DOI:
- 10.1103/PhysRevLett.125.190402

[15]

Coarse-grained quantum cellular automata

O. Duranthon
(
- LIS, Marseille and
- LPENS, Paris
)
,
Giuseppe Di Molfetta
(
- LIS, Marseille
)

- Phys.Rev.A 103 (2021) 032224
•
e-Print:
- 2011.04287
•
DOI:
- 10.1103/PhysRevA.103.032224

[16]

Entangled quantum cellular automata, physical complexity, and Goldilocks rules

Logan E. Hillberry
(
- Colorado School of Mines and
- Texas U.
)
,
Matthew T. Jones
(
- Colorado School of Mines
)
,
David L. Vargas
(
- Colorado School of Mines
)
,
Patrick Rall
(
- Texas U. and
- Caltech, IQI
)
,
Nicole Yunger Halpern
(
- Caltech, IQI and
- Harvard-Smithsonian Ctr. Astrophys. and
- Harvard U. and
- MIT and
- MIT, Cambridge, CTP and
- Maryland U.
)

et al.

- Quantum Sci.Technol. 6 (2021) 4, 045017,
- Quantum Sci.Technol. 6 (2021) 4, 045017
•
e-Print:
- 2005.01763
•
DOI:
- 10.1088/2058-9565/ac1c41

[17]

Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

- Phys.Rev.A 103 (2021) 5, 052203
•
e-Print:
- 2011.05597
•
DOI:
- 10.1103/PhysRevA.103.052203

[18]

Directed percolation in non-unitary quantum cellular automata

- Phys.Rev.Res. 3 (2021) 043167
•
e-Print:
- 2105.01394
•
DOI:
- 10.1103/PhysRevResearch.3.043167

[19]

Fermionic quantum cellular automata and generalized matrix-product unitaries

- J.Stat.Mech. 2101 (2021) 013107
•
DOI:
- 10.1088/1742-5468/abd30f

[20]

Entanglement in the Quantum Game of Life

Peter-Maximilian Ney
(
- Saarland U.
)
,
Simone Notarnicola
(
- INFN, Padua and
- Padua U., Astron. Dept. and
- U. Padua, Dept. Phys. Astron. and
- Padua U.
)
,
Simone Montangero
(
- INFN, Padua and
- Padua U., Astron. Dept. and
- U. Padua, Dept. Phys. Astron. and
- Padua U.
)
,
Giovanna Morigi
(
- Saarland U.
)

- Phys.Rev.A 104 (2022) 062607,
- Phys.Rev.A 105 (2022) 1, 012416
•
e-Print:
- 2104.14924
•
DOI:
- 10.1103/PhysRevA.105.012416

[21]

Entanglement dynamics and ergodicity breaking in a quantum cellular automaton

Kevissen Sellapillay
(
- Marseille, CPT and
- Toulon U.
)
,
Alberto D. Verga
(
- Marseille, CPT and
- Toulon U.
)
,
Giuseppe Di Molfetta
(
- LIS, Marseille
)

- Phys.Rev.B 106 (2022) 10, 104309
•
e-Print:
- 2207.05360
•
DOI:
- 10.1103/PhysRevB.106.104309

[22]

Three-Dimensional Quantum Cellular Automata from Chiral Semion Surface Topological Order and beyond

Wilbur Shirley
(
- Princeton, Inst. Advanced Study and
- Caltech, IQI
)
,
Yu-An Chen
(
- Maryland U., College Park
)
,
Arpit Dua
(
- Caltech, IQI
)
,
Tyler D. Ellison
(
- Washington U., Seattle and
- Yale U.
)
,
Nathanan Tantivasadakarn
(
- Harvard U.
)

et al.

- PRX Quantum 3 (2022) 3, 030326
•
e-Print:
- 2202.05442
•
DOI:
- 10.1103/PRXQuantum.3.030326

[23]

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models

et al.

- Nature 534 (2016) 7609, 667-670
•
DOI:
- 10.1038/nature18274

[24]

Probing many-body dynamics on a 51-atom quantum simulator

Hannes Bernien
(
- Harvard U.
)
,
Sylvain Schwartz
(
- Harvard U. and
- MIT, LNS
)
,
Alexander Keesling
(
- Harvard U.
)
,
Harry Levine
(
- Harvard U.
)
,
Ahmed Omran
(
- Harvard U.
)

et al.

- Nature 551 (2017) 579-584,
- Nature 551 (2017) 579-584
•
e-Print:
- 1707.04344
•
DOI:
- 10.1038/nature24622

[25]

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

- Phys.Rev.Lett. 120 (2018) 18, 180502
•
DOI:
- 10.1103/PhysRevLett.120.180502

1-25 of 93
1
2
3
4
25 / page